{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QDIFJMXZIBTABPYNJ75YRMTAP6","short_pith_number":"pith:QDIFJMXZ","schema_version":"1.0","canonical_sha256":"80d054b2f9406600bf0d4ffb88b2607fbadf4ef9b7ee2f719a6f9832fd634e1b","source":{"kind":"arxiv","id":"1204.6227","version":2},"attestation_state":"computed","paper":{"title":"On the spectral distribution of the free Jacobi process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Nizar Demni, Taoufik Hmidi, Tarek Hamdi","submitted_at":"2012-04-27T14:31:57Z","abstract_excerpt":"In this paper, we are interested in the free Jacobi process starting at the unit of the compressed probability space where it takes values and associated with the parameter values $\\lambda=1, \\theta =1/2$. Firstly, we derive a time-dependent recurrence equation for the moments of the process (valid for any starting point and all parameter values). Secondly, we transform this equation to a nonlinear partial differential one for the moment generating function that we solve when $\\lambda = 1, \\theta =1/2$. The obtained solution together with tricky computations lead to an explicit expression of t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.6227","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-04-27T14:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"c88cff18995c09419c3bb4b9ddc01f30e244b94538543dee45e717275169d0b8","abstract_canon_sha256":"be008fc667df240af9228c731bd026d381e791e38b4dc0219c7a2fc4553e00a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:35.166472Z","signature_b64":"ETeGABevrxlWLZYgsmuleqJBnbAtBAWoCnU67XMa6Nn/+guUoJxbxaFoyPHK7AZ61C5AEgzEvOQg5Gd9Hbv0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80d054b2f9406600bf0d4ffb88b2607fbadf4ef9b7ee2f719a6f9832fd634e1b","last_reissued_at":"2026-05-18T03:51:35.165723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:35.165723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the spectral distribution of the free Jacobi process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Nizar Demni, Taoufik Hmidi, Tarek Hamdi","submitted_at":"2012-04-27T14:31:57Z","abstract_excerpt":"In this paper, we are interested in the free Jacobi process starting at the unit of the compressed probability space where it takes values and associated with the parameter values $\\lambda=1, \\theta =1/2$. Firstly, we derive a time-dependent recurrence equation for the moments of the process (valid for any starting point and all parameter values). Secondly, we transform this equation to a nonlinear partial differential one for the moment generating function that we solve when $\\lambda = 1, \\theta =1/2$. The obtained solution together with tricky computations lead to an explicit expression of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6227","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.6227","created_at":"2026-05-18T03:51:35.165829+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.6227v2","created_at":"2026-05-18T03:51:35.165829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6227","created_at":"2026-05-18T03:51:35.165829+00:00"},{"alias_kind":"pith_short_12","alias_value":"QDIFJMXZIBTA","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QDIFJMXZIBTABPYN","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QDIFJMXZ","created_at":"2026-05-18T12:27:18.751474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6","json":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6.json","graph_json":"https://pith.science/api/pith-number/QDIFJMXZIBTABPYNJ75YRMTAP6/graph.json","events_json":"https://pith.science/api/pith-number/QDIFJMXZIBTABPYNJ75YRMTAP6/events.json","paper":"https://pith.science/paper/QDIFJMXZ"},"agent_actions":{"view_html":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6","download_json":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6.json","view_paper":"https://pith.science/paper/QDIFJMXZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.6227&json=true","fetch_graph":"https://pith.science/api/pith-number/QDIFJMXZIBTABPYNJ75YRMTAP6/graph.json","fetch_events":"https://pith.science/api/pith-number/QDIFJMXZIBTABPYNJ75YRMTAP6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6/action/storage_attestation","attest_author":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6/action/author_attestation","sign_citation":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6/action/citation_signature","submit_replication":"https://pith.science/pith/QDIFJMXZIBTABPYNJ75YRMTAP6/action/replication_record"}},"created_at":"2026-05-18T03:51:35.165829+00:00","updated_at":"2026-05-18T03:51:35.165829+00:00"}